Representing First-Order Causal Theories by Logic Programs

Nonmonotonic causal logic, introduced by Norman McCain and Hudson Turner, became a basis for the semantics of several expressive action languages. McCain's embedding of definite propositional causal theories into logic programming paved the way to the use of answer set solvers for answering queries about actions described in such languages. In this paper we extend this embedding to nondefinite theories and to first-order causal logic.Comment: 29 pages. To appear in Theory and Practice of Logic Programming (TPLP); Theory and Practice of Logic Programming, May, 201

The Small Number System

I argue that the human mind includes an innate domain-specific system for representing precise small numerical quantities. This theory contrasts with object-tracking theories and with domain-general theories that only make use of mental models. I argue that there is a good amount of evidence for innate representations of small numerical quantities and that such a domain-specific system has explanatory advantages when infants’ poor working memory is taken into account. I also show that the mental models approach requires previously unnoticed domain-specific structure and consequently that there is no domain-general alternative to an innate domain-specific small number system

Categories and the Foundations of Classical Field Theories

I review some recent work on applications of category theory to questions concerning theoretical structure and theoretical equivalence of classical field theories, including Newtonian gravitation, general relativity, and Yang-Mills theories.Comment: 26 pages. Written for a volume entitled "Categories for the Working Philosopher", edited by Elaine Landr

A conceptual model for the development of CSCW systems

Models and theories concerning cooperation have long been recognised as an important aid in the development of Computer Supported Cooperative Work (CSCW) systems. However, there is no consensus regarding the set of concepts and abstractions that should underlie such models and theories. Furthermore, common patterns are hard to discern in different models and theories. This paper analyses a number of existing models and theories, and proposes a generic conceptual framework based on the strengths and commonalities of these models. We analyse five different developments, viz., Coordination Theory, Activity Theory, Task Manager model, Action/Interaction Theory and Object-Oriented Activity Support model, to propose a generic model based on four key concepts common to these developments, viz. activity, actor, information and service

On the Triplet Frame for Concept Analysis

The paper has two objectives: to introduce the fundamentals of a triplet model of a concept, and to show that the main concept models may be structurally treated as its partial cases. The triplet model considers a concept as a mental representation and characterizes it from three interrelated perspectives. The first deals with objects (and their attributes of various orders) subsumed under a concept. The second focuses on representing structures that depict objects and their attributes in some intelligent system. The third concentrates on the ways of establishing correspondences between objects with their attributes and appropriate representing structures

An Object-Oriented Approach to Knowledge Representation in a Biomedical Domain

An object-oriented approach has been applied to the different stages involved in developing a knowledge base about insulin metabolism. At an early stage the separation of terminological and assertional knowledge was made. The terminological component was developed by medical experts and represented in CORE. An object-oriented knowledge acquisition process was applied to the assertional knowledge. A frame description is proposed which includes features like states and events, inheritance and collaboration. States and events are formalized with qualitative calculus. The terminological knowledge was very useful in the development of the assertional component. It assisteed in understanding the problem domain, and in the implementation stage, it assisted in building good inheritance hierarchies

The Nature and Function of Content in Computational Models

Much of computational cognitive science construes human cognitive capacities as representational capacities, or as involving representation in some way. Computational theories of vision, for example, typically posit structures that represent edges in the distal scene. Neurons are often said to represent elements of their receptive fields. Despite the ubiquity of representational talk in computational theorizing there is surprisingly little consensus about how such claims are to be understood. The point of this chapter is to sketch an account of the nature and function of representation in computational cognitive models

Towards a geometrical understanding of the CPT theorem

The CPT theorem of quantum field theory states that any relativistic (Lorentz-invariant) quantum field theory must also be invariant under CPT, the composition of charge conjugation, parity reversal and time reversal. This paper sketches a puzzle that seems to arise when one puts the existence of this sort of theorem alongside a standard way of thinking about symmetries, according to which *spacetime* symmetries (at any rate) are associated with features of the spacetime structure. The puzzle is, roughly, that the existence of a CPT theorem seems to show that it is not possible for a well-formulated theory that does not make use of a preferred frame or foliation to make use of a temporal orientation. Since a manifold with only a Lorentzian metric can be temporally orientable --- capable of admitting a temporal orientation --- this seems to be an odd sort of necessary connection between distinct existences. The paper then suggests a solution to the puzzle: it is suggested that the CPT theorem arises because temporal orientation is unlike other pieces of spacetime structure, in that one cannot represent it by a tensor field. To avoid irrelevant technical details, the discussion is carried out in the setting of classical (rather than quantum) field theory, using a little-known classical analog of the CPT theorem

First-Order Logical Duality

From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models can be topologized in such a way that the theory can be recovered from its space of models. The situation can be cast as a formal duality relating two categories of syntax and semantics, mediated by homming into a common dualizing object, in this case 2. In the present work, we generalize the entire arrangement from propositional to first-order logic. Boolean algebras are replaced by Boolean categories presented by theories in first-order logic, and spaces of models are replaced by topological groupoids of models and their isomorphisms. A duality between the resulting categories of syntax and semantics, expressed first in the form of a contravariant adjunction, is established by homming into a common dualizing object, now \Sets, regarded once as a boolean category, and once as a groupoid equipped with an intrinsic topology. The overall framework of our investigation is provided by topos theory. Direct proofs of the main results are given, but the specialist will recognize toposophical ideas in the background. Indeed, the duality between syntax and semantics is really a manifestation of that between algebra and geometry in the two directions of the geometric morphisms that lurk behind our formal theory. Along the way, we construct the classifying topos of a decidable coherent theory out of its groupoid of models via a simplified covering theorem for coherent toposes.Comment: Final pre-print version. 62 page

Platonic model of mind as an approximation to neurodynamics

Hierarchy of approximations involved in simplification of microscopic theories, from sub-cellural to the whole brain level, is presented. A new approximation to neural dynamics is described, leading to a Platonic-like model of mind based on psychological spaces. Objects and events in these spaces correspond to quasi-stable states of brain dynamics and may be interpreted from psychological point of view. Platonic model bridges the gap between neurosciences and psychological sciences. Static and dynamic versions of this model are outlined and Feature Space Mapping, a neurofuzzy realization of the static version of Platonic model, described. Categorization experiments with human subjects are analyzed from the neurodynamical and Platonic model points of view